It is known that, as the number of antennas gets large, both \(\Vert  \hat{\mathbf {h}}_{tm}^{k} \Vert ^2\)  and \(| \hat{\mathbf {h}}_{tm}^{kH} \hat{\mathbf {h}}_{ti}^{k} |^2\)  converge almost surely (a.s.) to their deterministic equivalents [1]}.
Evaluating the deterministic equivalents as in [1]} and plugging into the SINR expression instead of the original terms, we can find an approximation to the SINR in the high antenna regime.
As \(N\)  gets large, the SINR with MRC converges almost surely (\(\rho _{tm}^k \stackrel{\text{a.s.}}{\longrightarrow } \overline{\rho }_{tm}^k\) ) to
\(\overline{\rho }_{tm}^k &= \dfrac{N {\tt Sig}_{tm}^k }{\epsilon _{tm}^k \left( N_0/P + {\tt NCoh}_{tm}^k \right) + {\tt Coh}_{tm}^k},\) 
